The document discusses frequency distributions and methods for organizing and presenting both quantitative and categorical data. It provides examples of constructing frequency distributions and histograms for quantitative data, including determining class intervals and boundaries. For categorical data, it demonstrates creating frequency tables and bar or pie charts to summarize ratings data. The goal is to condense raw data into more useful forms for analysis and visual interpretation.

1. GOALS
1. Organize qualitative data into a frequency table.
2. Present a frequency table as a bar chart or a pie
chart.
3. Organize quantitative data into a frequency
distribution.
4. Present a frequency distribution for quantitative
data using histograms, frequency polygons, and
cumulative frequency polygons.
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-1

2. Tabulating Numerical Data:
Frequency Distributions
What is a Frequency Distribution?
 A frequency distribution is a list or a table …
 containing class groupings (ranges within which
the data fall) ...
 and the corresponding frequencies with which
data fall within each grouping or category
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-2

3. Why Use a Frequency Distribution?
 It is a way to summarize numerical data
 It condenses the raw data into a more
useful form...
 It allows for a quick visual interpretation of
the data
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-3

4. Class Intervals
and Class Boundaries
 Each class grouping has the same width
 Determine the width of each interval by
Width of interval @ range
number of desired class groupings
 Usually at least 5 but no more than 15
groupings
 Class boundaries never overlap
 Round up the interval width to get desirable
endpoints
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-4

5. EExxaammppllee:: HHoonnddaa AAuuttoo RReeppaaiirr
TThhee mmaannaaggeerr ooff HHoonnddaa AAuuttoo
wwoouulldd lliikkee ttoo hhaavvee aa bbeetttteerr
uunnddeerrssttaannddiinngg ooff tthhee ccoosstt
ooff ppaarrttss uusseedd iinn tthhee eennggiinnee
ttuunnee--uuppss ppeerrffoorrmmeedd iinn tthhee
sshhoopp.. SShhee eexxaammiinneess 5500
ccuussttoommeerr iinnvvooiicceess ffoorr ttuunnee--uuppss.. TThhee ccoossttss ooff ppaarrttss,,
rroouunnddeedd ttoo tthhee nneeaarreesstt ddoollllaarr,, aarree lliisstteedd oonn tthhee nneexxtt
sslliiddee..
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-5

6. EExxaammppllee:: HHoonnddaa AAuuttoo RReeppaaiirr
SSaammppllee ooff PPaarrttss CCoosstt ffoorr 5500 TTuunnee--uuppss
91 78 93 57 75 52 99 80 97 62
71 69 72 89 66 75 79 75 72 76
104 74 62 68 97 105 77 65 80 109
85 97 88 68 83 68 71 69 67 74
62 82 98 101 79 105 79 69 62 73
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-6

7. Tabular Summary:
Frequency and Percent Frequency
PPaarrttss
CCoosstt (($$))
5500--5599
6600--6699
7700--7799
8800--8899
9900--9999
110000--110099
PPaarrttss
FFrreeqquueennccyy
22
1133
1166
77
77
55
5500
PPeerrcceenntt
FFrreeqquueennccyy
44
2266
3322
1144
1144
1100
110000
((22/5500))110000
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-7

8. Graphical Summary: Histogram
18
16
14
12
10
8
6
4
2
Parts
Cost ($)
Frequency
50-59 60-69 70-79 80-89 90-99 100-110
TTuunnee--uupp PPaarrttss CCoosstt
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-8

9. Histogram (Continued)
 Symmetric
 Left tail is the mirror image of the right tail
 Example: heights and weights of people
Relative Frequency
.35
.30
.25
.20
.15
.10
.05
0
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-9

10. Histogram (Continued)
 Moderately Skewed Left
 A longer tail to the left
 Example: exam scores
Relative Frequency
.35
.30
.25
.20
.15
.10
.05
0
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-10

11. Histogram (Continued)
 Moderately Right Skewed
 A Longer tail to the right
 Example: housing values
Relative Frequency
.35
.30
.25
.20
.15
.10
.05
0
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-11

12. Histogram (Continued)
 Highly Skewed Right
 A very long tail to the right
 Example: .35
executive salaries
.30
Relative Frequency .05
.25
.20
.15
.10
0
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-12

13. Frequency Distribution Example
Example: A manufacturer of insulation randomly
selects 20 winter days and records the daily
high temperature
24, 35, 17, 21, 24, 37, 26, 46, 58, 30,
32, 13, 12, 38, 41, 43, 44, 27, 53, 27
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-13

14. Frequency Distribution Example
(continued)
 Sort raw data in ascending order:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
 Find range: 58 - 12 = 46
 Select number of classes: 5 (usually between 5 and 15)
 Compute class interval (width): 10 (46/5 then round up)
 Determine class boundaries (limits): 10, 20, 30, 40, 50, 60
 Compute class midpoints: 15, 25, 35, 45, 55
 Count observations assign to classes
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-14

15. Frequency Distribution Example
Data in ordered array:
(continued)
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Relative
Frequency Percentage
Class Frequency
10 but less than 20 3 .15 15
20 but less than 30 6 .30 30
30 but less than 40 5 .25 25
40 but less than 50 4 .20 20
50 but less than 60 2 .10 10
Total 20 1.00 100
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-15

16. Tabulating Numerical Data:
Cumulative Frequency
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Class
Data in ordered array:
Frequency Cumulative
Percentage Cumulative
Percentage
Frequency
10 but less than 20 3 15 3 15
20 but less than 30 6 30 9 45
30 but less than 40 5 25 14 70
40 but less than 50 4 20 18 90
50 but less than 60 2 10 20 100
Total 20 100
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-16

17. Graphing Numerical Data:
The Histogram
 A graph of the data in a frequency distribution
is called a histogram
 The class boundaries (or class midpoints)
are shown on the horizontal axis
 the vertical axis is either frequency, relative
frequency, or percentage
 Bars of the appropriate heights are used to
represent the number of observations within
each class
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-17

18. Histogram Example
Histogram: Daily High Temperature
7
6
5
4
3
2
1
0
5 15 25 35 45 55 65
Frequency
Frequency
Class Midpoints
Class
Midpoint
10 but less than 20 15 3
20 but less than 30 25 6
30 but less than 40 35 5
40 but less than 50 45 4
50 but less than 60 55 2
(No gaps
between
bars)
Class
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-18

19. Graphing Numerical Data:
The Frequency Polygon
Frequency Polygon: Daily High Temperature
7
6
5
4
3
2
1
0
5 15 25 35 45 55 65
Frequency
Class Midpoints
Class
Frequency
Class
Midpoint
10 but less than 20 15 3
20 but less than 30 25 6
30 but less than 40 35 5
40 but less than 50 45 4
50 but less than 60 55 2
(In a percentage
polygon the vertical axis
would be defined to
show the percentage of
observations per class)
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-19

20. Graphing Cumulative Frequencies:
The Ogive (Cumulative % Polygon)
Ogive: Daily High Temperature
100
80
60
40
20
0
10 20 30 40 50 60
Cumulative Percentage
Class Boundaries (Not Midpoints)
Class
Cumulative
Percentage
Lower
class
boundary
Less than 10 0 0
10 but less than 20 10 15
20 but less than 30 20 45
30 but less than 40 30 70
40 but less than 50 40 90
50 but less than 60 50 100
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-20

21. Categorical Data
  Categorical data involves categories or
 groups.
  These can be made without the fear of
 their order to be disturbed
 i.e. sex, age, marital status.
  It covers the following topics:
 Frequency Distribution
 Graphs
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-21

22. Example: Marada Inn
Guests staying at Marada Inn were
asked to rate the quality of their
accommodations as being excellent,
above average, average, below average, or
poor. The ratings provided by a sample of 20 guests are:
BBeellooww AAvveerraaggee
AAbboovvee AAvveerraaggee
AAbboovvee AAvveerraaggee
AAvveerraaggee
AAbboovvee AAvveerraaggee
AAvveerraaggee
AAbboovvee AAvveerraaggee
AAvveerraaggee
AAbboovvee AAvveerraaggee
BBeellooww AAvveerraaggee
PPoooorr
EExxcceelllleenntt
AAbboovvee AAvveerraaggee
AAvveerraaggee
AAbboovvee AAvveerraaggee
AAbboovvee AAvveerraaggee
BBeellooww AAvveerraaggee
PPoooorr
AAbboovvee AAvveerraaggee
AAvveerraaggee
AAvveerraaggee
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-22

23. FFrreeqquueennccyy DDiissttrriibbuuttiioonn
RRaattiinngg FFrreeqquueennccyy
PPoooorr
BBeellooww AAvveerraaggee
AAvveerraaggee
AAbboovvee AAvveerraaggee
EExxcceelllleenntt
22
33
55
99
11
TToottaall 2200
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-23

24. BBaarr GGrraapphh
10
9
8
7
MMaarraaddaa IInnnn QQuuaalliittyy RRaattiinnggss
Excellent Frequency
Poor Below
Average
Average Above
Average
Rating
6
5
4
3
2
1
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-24

25. PPeerrcceennttaaggee FFrreeqquueennccyy DDiissttrriibbuuttiioonn
RRaattiinngg PPeerrcceennttaaggeess
PPoooorr
BBeellooww AAvveerraaggee
AAvveerraaggee
AAbboovvee AAvveerraaggee
EExxcceelllleenntt
1100
1155
2255
4455
55
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-25

26. PPiiee CChhaarrtt
MMMMaaaarrrraaaaddddaaaa IIIInnnnnnnn QQQQuuuuaaaalllliiiittttyyyy RRRRaaaattttiiiinnnnggggssss
Poor
10%
Below
Average
15%
Average
25%
Excellent
5%
Above
Average
45%
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-26

27. PPeerrcceennttaaggee FFrreeqquueennccyy DDiissttrriibbuuttiioonn
RRaattiinngg AAnngglleess
PPoooorr
BBeellooww AAvveerraaggee
AAvveerraaggee
AAbboovvee AAvveerraaggee
EExxcceelllleenntt
3366
5544
9900
116622
1188
CCuummiillaattiivvee AAnngglleess
3366
9900
118800
334422
336600
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 2-27